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White has to protect the pawn with either Kg6 or Bb3/Be8. Now, I can see pretty easily that either bishop move is going to lose since black then has time to march the king over to e7 to both protect the rook from white's king, and to prepare a triple attack on the pawn. Let's just outline the problem with the bishop moves:1. Bb3 Kc7 (Kc8 or Kc6 win too)2. Kg6 Kd73. Kf6Here, Kg7 just concedes immediately since black's king reaches e7 and can't be harrassed.Continuing:3. .....Kd6 (to guard e5)4. Ba2 Ne55. Bb3 Nd7 and the white king must give up control of e7 to black's king. The pawn can't now be saved.No better is the plan starting with 1.Be8, though black has a quicker win since white loses a tempo to black's reply:1. Be8 Ne5 and the white king loses a tempo by having to navigate around g6, and the pawn falls immediately.So, the first move must be Kg6:1. Kg6Obviously, white's threat is Kg7 followed by f8Q to win the rook. I don't see how black can prevent this with any move other than Ne5 immediately attacking the pawn twice. Continuing:1. .....Ne5 (with check)2. Kf6!Surely the only move. White cannot play Kg7 since black will capture with the rook at f7. Now black has a problem- he can't take the pawn with the rook without losing the knight (the resulting R vs B ending is a technical draw). If black checks from g4, white just plays Kg7/e7 to win the rook for a pawn. This leaves only the pawn capture via Nf7:2. .....Nf73. Ke7!I will discuss 3.Kg7 below. The point is that black can move the rook to safety and attack the bishop by playing Ra8, maintaining his rook edge. With 3.Ke7, white has a reply ready:3. .....Ra84. Bb3!A double threat- if black moves the knight, white skewers the king a rook with Bd5. The position is even a bit more elegant than it appears- 4.Bb3 is an only move. I considered moving black's rook at move 4 attacking the bishop if white had played a move like 4.Bc2 planning Be4+, but white can always check the king to save the bishop and then take the knight. Black has only one hope- to use the knight to black the coming skewer:4. .....Ne55. Bd5 Nc66. Kd6If white tries Kd7, black can just check from d8 and then play Kc7/b6 to save both of his pieces. With Kd6, white can keep pressure on the pinned knight:6. .....Rc87. Kc5!This is the truly beautiful part of this problem. As black tries to protect the knight with the rook from either c8 or a6, white moves to take away the only other square open to the black king that is not break the rook's guard on c6. If black had played 6. ...Ra6, white just moves the bishop along d5/h1 diagonal, and here with Rc8, white moves to take away b6 and force Kc7. No matter how you try it, black cannot both guard the knight with the king and rook and remove the pin. This is drawn.
This puzzle need good calculation and visualization, white is force to play 1.Kg6 to support pawn promotion. If 1...Ne5+ 2.Kf6 attacking the knight. If 2..Rxf7 3. Kxe5 (draw bishop vs rook). If 2..Nxf7 then 3.Re7 attacking both rook and knight, black attack white bishop with 3..Ra8 and white can save draw with Bb3 attacking Bd5+ and the knight.
The key idea for a draw in a bishop rook endgame is for the weaker side K to reach the corner whose color is different from the bishop. Here white with a white bishop has to reach black h8 corner to draw after exchanging pawn for N.1.Bb3!>A-1....Ne5.2.Kh6!.Nxf7.3.Kg7! Winning the knight when the rook moves. Of course giving up the rook is a draw.Black R cannot attack the white B as it is shielded by the black king on b file! So, 3...R move.4.Kxf7 draws. >B-1.....Kc7.2.Kg6!.Ne5+.3.Kg7.>>B1-3..Nxf7.4.Kxf8 draw>>B2.3..rook moves.4.f8= Q.Rxf8.5.Kxf8 draw>>B3.3..Nd7! This is the trickiest.4.Be6!! Rd8.5.Bxd7.Kxd7.6.f8=Q.Rxf8.7.Kxf8 draw. Here black has to be careful and not try to win lest the bishop shuts out the rook from f8 by Be8!Harry
1Bb3 ne5 2Kh6 nf7 3 Kg7 knight gone
Whites plan here is to go and attack f8 with the king. Then it's problematic for black to defend it, since ha shall have neither Nd7 nor Ng6. To prevent Nd7 is the role of the bishop here. And the king will take knight after Ng6.Neither is it a winning option for black to move his rook, since this leads to f8=Q and black must give rook.Conclusion:The pawn must be taken.Either knight takes it or rook takes it, white king will in both cases take the rook.This is why this can't be anything else than a draw.The obvious first move is:1. Kg6 Ne5+ (what else?)2. Kg7 Nxf7 (Ng6 Kxg6 Rxf7 Kxf7)3. Kxf8
1.Kg6 (threatening Ke7) Ne5+ 2.Kf6 Nc6 (2.-Nxf7 3.Ke7 draws) 3.Bxc6+ Kxc6 4.Ke7 draws
Bb3! the rest are easy....
This position reminds me of an earlier composition from Pogosyants (8/8/1P3k2/7K/4n3/5r2/7B/8, =, E. Pogosyants, Shakhmaty v SSSR, 1983) with a similar balance at the end!!This one goes:1. Kg6 Ne7 2. Kf6 Nxf7 3. Ke7 Ra8 4. Bb3 Ne5 5. Bd5+ Nc6+ 6. Kd6 Rc8 7. Kc5 and white drawsCheers!
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